Lubricant oils are used for internal combustion engines, transmissions, and other machinery in order to smooth the action. Particularly, high performance is demanded of the lubricant oils for internal combustion engines (engine oils) along with higher performance and higher output of the internal combustion engines, and severer operation conditions, and the like. Accordingly, in order to satisfy such required performances, a variety of additives such as a wear-resistant agent, a metallic detergent, an ash-free dispersant, and an antioxidant are blended with the conventional engine oil (see Patent Literatures 1 to 3 below, for example.). Recently, a demand for fuel efficiency performance of the lubricant oil has been increased more and more, and use of a high viscosity index base oil or use of a variety of friction modifiers has been examined (see Patent Literature 4 below, for example.).